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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    For any real number y the greatest integers not exceeding y is denoted by [y]. If \[f:R\to R\] is defined by \[f(x)=[2x]-2[x]\] for \[x\in R,\] then the range of f is

    A)  \[\{x\in R:x>0\}\]

    B)  \[\{x\in R:x\le 0\}\]

    C)  \[\{x\in R:0\le x\le 1\}\]

    D)  \[\{0,\,1\}\]

    Correct Answer: D

    Solution :

    We have, \[f(x)=[2x]-2[x]\] For \[x=0,\,f(0)=[0]-2[0]=0\] For \[x=0.45,\,f(0.45)=[0.90]-2[0.45]\] \[=0-0=0\] For \[x=0.5,\,f(0.5)=[1.0]-2[0.5]\] \[=1-0=1\] For \[x=0.99,\,f(0.99)=[1.98]-2[0.99]\] \[=1-0=1\] So, the range of f is \[\{0,1\}\]


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